SREs distort spectrum recorded by a PCD and is nearly impossible to correct. Photon counting x-ray detectors (PCXDs) have the potential to significantly improve x-ray computed tomography (CT) by reducing dose, providing quantitative material decomposition, and enabling K-edge imaging using high-Z contrast agents such as Gd, Au or Bi. A major problem, however, is the spectral response (SR) or the distortion of the spectrum due to the following physical effects: a finite energy-resolution, Compton scattering, charge-sharing, and K escape. These effects are independent of the incident count rate; thus, the transmitted spectrum is always distorted. If uncompensated, they result in image artifacts and inaccurate material decomposition.
In current research, a computational model of the SR, or a spectral response function (SRF), was developed based on measurements with a synchrotron. The SRF was then integrated into a forward imaging process and a maximum likelihood method was proposed to estimate line integrals of the x-ray attenuation coefficients of basis functions. The Nelder-Mead method, used as an optimization method in this research, requires numerous function evaluations and is often slower to converge than gradient-based methods. Even though the Nelder-Mead method usually converges to the minimum of the cost function, there are not many theorems from optimization theory to guarantee convergence in general cases.
It would therefore be advantageous to provide a system for correcting for the SREs recorded by PCDs.